:-S Follow on to induction question (1 Viewer)

[Grey Council]

Hokay, just proved that the sum of the first n squares is equal to:
n(n+1)(2n+1) / 6

the question now says:
Use this result to evaluate 2^2 + 4^2 + 6^2 + ... + 100^2

 

[Faera]

hmm. *guesses ramdomly*

perhaps...

Try to write the 2 squared + 4 squared + 6 squared pattern as sums of squares...

eg 2 squared = 1 squared + 1 squared...

4 squared = 2 squared x 4

o.0

or maybe not...

 

[Grey Council]

:-S

 

[Faera]

gah got it.

Take 2 squared out as a common factor.
*was blind*


i didnt see it at first, coz when i divided 64/4, i managed to wind up with 18... its too early in the morning.

 

[Grey Council]

hee, true.

its 4.1^2 + 4.2^2 +...+4.50^2



Ta Faera

 

[Grey Council]

what're you doing in this forum?

blah, I s'pose your right. thanks

 

[Estel]

Without wings: I'm sure your incursion has offended numbers beyond count...
[for someone like you ... if you do 4u I guess that wasn't a clever thing to say ]

Would you be allowed to assume that formula in a question? Eg. integration by first principles (assuming they didn't give it to you).

 

[Grey Council]

whaa?

Integration by first principles?

Where does integration come into this? Sorry, you've lost me there.

however, I've seen this in a few trial papers as an induction question. So they usually ask you to prove it via induction, then they ask you related question. Its near the end, the ones I've seen have all been absolute last question.

 

[CrashOveride]

Grey Council: Are you looking at past trial papers from your school? Where are people geting trial papers from etc. ?

Yeah ive seen that question before as well ^_^

 

[Grey Council]

I'm looking at past trial papers from all over the state. Ruse, Grammar, my school, Scots, sghs, catholic, independant, neap. Those are the ones I've done/seen so far for 3u maths these holidays.

Heh, I have multiples for a few of them, esp Grammar and my own school.
You know, out of all those papers, imho my school sets the hardest. @_@ Just my luck, hey?

hanyway, I got them from my old tutor, this site and a cd I bought off a past student. Hrm

 

[Slidey]

How does one "integrate by first principles"? I thought there was no hard and fast method for integration, besides the common rule "if f'(x)=x^n, then f(x)=x⁽ⁿ⁺¹⁾/(n+1)"?

 

[Xayma]

How does one "integrate by first principles"? I thought there was no hard and fast method for integration, besides the common rule "if f'(x)=x^n, then f(x)=x⁽ⁿ⁺¹⁾/(n+1)"?

"If f'(x)=xⁿ, then f(x)=xⁿ⁺¹/(n+1) +C"

 

[Estel]

First principles integration = integration using a manual limiting process... i.e. some of those questions you tend to see as Q6 or Q7 where you have to prove that formula by induction first.